Analytic variance-covariance value-at-risk (VaR) is an established technique for measuring exposure to market-based financial risk. A recent and comprehensive overview of a specific VaR methodology is given in "RiskMetrics.TM.--Technical Document," Fourth Edition, Dec. 18, 1996, by J. P. Morgan/Reuters. Given a description of the market characteristics and a statement of the user's transaction portfolio, the objective of VaR is to determine how much financial value might be lost over a given time period, with a given level of probability, in a given currency.
This analytic form of VaR begins by replacing a portfolio, or the trades within it, with a set of component asset flows (known generically as "cashflows") reflecting both those trades' current values and their risk attributes. This initial process is sometimes separately referred to as "shredding" the trades. The next step in determining VaR is cashflow allocation. Cashflow allocation distributes cashflows (which can be in any currency, commodity, or other price risk source) amongst a set of standardized maturities and credit levels at future specified time intervals, for the markets wherein the cashflows are traded, again preserving their value and risk characteristics. The future time intervals, such as 1 month, 3 months, 6 months, and 12 months, are generally a constant amount of time into the future, and hence are known as constant maturity tenors (or CMTs). The combination of a tenor and a cashflow type is termed a "vertex." For example, six-month Libor Deutschemark and two-year U.S. dollar swap market flows are possible vertices. The "edges" of a vertex are its different attributes, such as currency, amount, and tenor. The complete process of translating trades into vertex cashflows is generally termed "mapping." Mapping provides a representation of the original portfolio in the context of a standardized set of cashflows. The vertices onto which the cashflows are mapped are also used as the index set of a covariance matrix of the market values of the cashflows, which describes the current market risk characteristics to a reasonable degree of detail. Having thus arrived at the "cashflow map" (i.e., the net result of mapping a portfolio of trades onto the benchmark cashflows), the cashflow map is then combined with the covariance matrix, along with a time horizon and a probability confidence level, yielding the desired result, namely, the value-at-risk (VaR) number. The VaR value indicates the dollar (or other currency) amount that could be lost, within the time period of the cashflows, with a given level of confidence.
The current state of cashflow allocation art is given rather extensive definition in "RiskMetrics.TM.--Technical Document," cited above, at pp. 117-121. One of the key issues in cashflow allocation is allocation of a cashflow that has a timing (date of execution) that lies between the timing of the two "closest" vertices. RiskMetrics teaches an allocation that splits such a cashflow between those two nearby vertices. This allocation may involve preserving net present value, VaR, duration, or some other criteria or combinations of these and/or other such criteria. This allocation method (to two vertices) is herein termed a "regular allocation." Implicitly also, if the original cashflow's timing does not lie between two vertices, all of it is simply allocated to the most nearby vertex. For example, a cashflow due to occur in one week would all be allocated to the 1 month vertex in RiskMctrics, since this is the earliest vertex for data which is provided in the commercially available covariance matrices. Likewise, a 32-year cashflow would be allocated entirely to the 30-year vertex, since this is the longest time vertex now used.
The regular cashflow allocation methodology may be diagrammatically illustrated as in FIG. 1. In this figure, there are five cashflows that are each to be allocated over vertices involving only three edge values, indicated as vertices 1, 2, and 3, each having a constant maturity time relative to an analysis date, such as 1 month, 3 months, and 6 months. It should be noted that the vertices here may be sets of vertices.
The first cashflow (#1) has a tenor earlier than any vertex. The regular allocation method assigns 100% of this cashflow (possibly adjusted for the present value of money) to this vertex #1, generally following the RiskMetrics methodology. The cashflows #2, #3, and #4 each lie between a pair of vertices. Therefore, the regular allocation divides each of these cashflows between the two most nearby vertices. Thus, cashflow #2 is allocated between vertex 1 and vertex 2; cashflows #3 and #4 are both allocated between vertices 2 and 3. The last cashflow #5 has a tenor longer than any vertex, so it is entirely allocated to the last vertex 3.
However, some institutions employing analytic and other forms of VaR analysis are interested in separating the risks of their income statement for the next period from the risks of their balance sheet at the end of that period. That is, there is a desire to obtain a number of VaR results from a single portfolio, with each VaR limited to a specific time period. For example, on January 1, a company may have a financial quarter ending on the next March 31, and its corporate treasury officers may have an interest in keeping the VaR calculated for a trading portfolio from the period from the January 1, until March 31 separate from the VaR calculated for that same portfolio after that date. However, present techniques in analytic VaR do not permit such separation because their prescribed means of cashflow mapping do not recognize such separations of time periods. Instead, the cashflows of portfolio are simply allocated onto the various tenors, irrespective of the specific dates of interest, such as an end of financial quarter.
As a concrete example, suppose that a fixed-price contract (a contract to buy or sell periodically in the future) is entered into by a corporate entity. To be more specific, suppose that the corporate entity is a jewelry manufacturer and that it has contracted to purchase 100 oz. of gold every month for the next two years, from a supplier at the fixed price of US$400 per oz. (regardless of the market price). Using conventional VaR methodology, this contract would be decomposed into "cashflows" involving inflows of 100 oz. of gold each month and outflows of $40,000 every month; this is the "shredding" of the contract into component cashflows. Next, a regular allocation would allocate each component cashflow to various vertices. For example, the U.S. dollar and gold vertices are typically defined for maturities at 1 month, 3 months, 6 months, 12 months, and 24 months from the date of analysis. Under a regular allocation, every gold and U.S. dollar cashflow that occurs between two vertices (relative to the date of analysis) will always be partially allocated between these two vertices. For example, the gold cashflow occurring at 5 months from the analysis date will be divided between the 3 months and 6 months' vertices, with more of the cashflow being allocated to the 6 month vertex. In a similar fashion, the remaining gold and U.S. dollar cashflows in this example will be allocated to their surrounding vertex maturities.
Now suppose further that all cashflows occur on the 20.sup.th of each month, that the contract runs from January of this year through December of the following year, that the analysis is being performed on February 10 of this year, and that the corporation's fiscal year ends on September 30 of this year. In a regular allocation, the cashflow occurring September 20 (7 months and 10 days from the analysis date) will be allocated between the 6 month and 12 month vertices, which correspond, on the analysis date to August 20, and February 10 of the next year, respectively. However, if the corporation's fiscal year ends on September 30 of the current year, it is desirable for the corporation to separate its calculation of VaR before its end-of-fiscal-year ("income statement risk") from that after end-of-fiscal-year ("balance sheet risk"). Conventional VaR technology does not provide the means of such separation of VaR into these different types of risks.
The analysis is complicated by the fact that vertices are, as noted above, defined by constant maturity tenors. This means that the time periods involved in vertex definition are a constant period of time ahead from the current point of analysis, for example, always three months or six months from the date the VaR analysis is performed. Correspondingly, this implies that the dates associated with the vertices shift forward one day as each day passes. On the other hand, most financial instruments lead to cashflows that occur on fixed dates, dates which do not shift forward as do the CMTs. This temporal mis-match between vertices and cashflows causes constantly shifting cashflow maps, as the time at which the VaR analysis is conducted constantly changes. That is, the VaR result produced on today for a given portfolio will be different from the VaR result produced tomorrow. Moreover, the future dates in which corporations are interested, for example the fiscal year ends for separation of income statement verses balance sheet risk, tend to be of the fixed-date variety. Thus, present methods do not enable the accurate analysis of income and balance sheet risk.
Various solutions have been proposed and considered to the problem of properly allocating cashflows for performing the VaR analysis. One approach is that of the accountants, namely to separate the financial portfolio by types of financial instruments, specifically income-statement verses balance-sheet instruments, and then separately shred, allocate and compute the VaR for each subset. This is most commonly done according to the maturity of the instrument. For risk analysis purposes, however, this is not an effective technique. The approach fails because instruments that mature after the end of the fiscal year can nonetheless generate cashflows before the end of the fiscal year, such as in the jewelry company example above. Occasionally, but more rarely, the opposite is also true.
Separation of cashflows by time period is another possible method. All cashflows before the end of the fiscal year are allocated by themselves, and all cashflows after the end of the fiscal year are separately allocated, and a VaR computation is performed for each set. But this approach also fails, because the prescribed mapping methodologies allow amounts to be allocated to vertices on both sides of the fiscal year. In the jewelry company example above, on March 30, a cashflow on September 20 occurring before the end of the fiscal year on September 30 might be partially allocated to a vertex at December 31, well after the end of the fiscal year. Thus segregating cashflow portfolios fails also.
Another solution is to define new, "synthetic" vertices just prior to and after the fiscal year end date. For instance, if the fiscal year ended September 30, one synthetic vertex is created at September 30 and another is created at October 1. While this approach may prevent the allocation of cashflows across the fiscal year barrier, as in the previous approach, there are still serious shortcomings to this method. First, the synthetic vertices, unlike the other vertices, are not CMTs, and so the correlation estimates (which are necessary for the VaR calculation) between these and the other vertices will be constantly changing as time passes, even if the markets are completely quiescent. Second, the high correlation between the two synthetic vertices may itself cause instability in the allocation calculations. Third, there may still occasionally be some evaluation dates where cashflows fall between the synthetic vertices, and the regulation allocation between these vertices may still be erroneous (without error bound, since the cashflows are of unbounded size).
Accordingly, it is desirable to provide a computer system and computer implemented method that provides for the analytically correct allocation of cashflows into any arbitrary number of distinct time periods, and thereby allows for the correct determination of VaR for each such time period. It is further desirable to provide a system and method for correctly determining income sheet and balance sheet risk for any portfolio of transactions.